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Please Solve RD Sharma Class 12 Chapter Function Exercise 2.4 Question 15 Maths Textbook Solution.

Answers (1)

Answer:

$f^{-1}\left ( 43 \right )2,f^{-1}\left ( 163 \right )=4$

Given:

$f:N\rightarrow N$ is a function defined as $f\left ( x \right )=9x^{2}+6x-5$ .

Hint:

The function should be an identity function.

Solution:

Let $y=f\left ( x \right )=9x^{2}+6x-5$

$y=9x^{2}+6x+1-1-5$

$y=\left (9x^{2}+6x+1 \right )-6$

$y=\left ( 3x+1 \right )^{2}-6$

$y+6=\left ( 3x+1 \right )^{2}$

$\sqrt{y+6}=\left ( 3x+1 \right )$

$\sqrt{y+6}-1=3x$

(Let )

Now,

=y+6-6

Identity function.

Identity function

Since andare identity functions.

Thus is invertible.

So,

Now,

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